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The Duhem-Quine thesis is that it's impossible to test a scientific hypothesis in isolation, because any empirical test requires implicit auxiliary hypotheses. Such auxiliary hypotheses may include assumptions about initial conditions, other scientific hypotheses concerning the function of experimental apparatus, or even metaphysical presuppositions on the nature of observation.

The Duhem-Quine thesis is often referred to as the Duhem-Quine problem, because it appears to undermine the authority of science to reveal general facts about the universe. That is, it implies that we can never pin the blame for a failed prediction on any particular hypothesis--all we know, so to speak, is that something is rotten in the state of Denmark. In particular, the Duhem-Quine thesis is often held up as a refutation of Karl Popper's criterion of falsifiability, and it's this claim I wish to address here.

Normally, the logic of falsification is presented as a case of modus tollens, but it's perhaps more helpful to consider it in as the retransmission of falsity in a valid argument. That is, just as truth is transmitted from premises to conclusion in a valid argument, so falsity is retransmitted from conclusion to premises, i.e. if the conclusion is false, then at least one of the premises must be false.

Where 'H' is a scientific hypothesis and 'E' is some evidence, we might say that 'not-E' falsifies the hypothesis if, and only if,

H ⊨ E

However, this is a naive understanding of falsification. As the Duhem-Quine thesis reminds us, such a deduction implicitly depends on many auxiliary hypotheses, e.g. initial conditions. We'll label these auxiliary hypotheses 'A1' to 'An'.

H & (A^1 & ... A^n) ⊨ E

Now we have a rather explicit representation of the Duhem-Quine problem: 'not-E' no longer entails 'not-H'. In this case, 'not-E' falsifies the entire conjunction of 'H' and 'A1' through 'An '--at least one member of that conjunction must be false. However, there is no logical procedure to determine which premise(s) is responsible for the falsification, and there are multiple logically permissible moves to restore consistency. Perhaps 'H' is just false, or maybe 'H' is true and 'A7' is the problem; maybe they're all false.

However, I want to suggest this formulation of the logic of falsification is inappropriate, especially given Popper's own views on the nature of observation. In particular, Popper stressed that all observation is theory-laden. He argued that even a simple statement like 'there is a cup of water here on the table' is theoretically-loaded. Things like tables, water, and cups are defined by their general behaviour; even the idea of something being here involves rather complex assumptions about space and time. For Popper, then, there was nothing infallible or epistemologically foundational about observation; rather, reports of observation are highly conjectural attempts to capture discrete facts.

My claim, then, is that from a Popperian perspective, rather than lumping the auxiliary hypotheses with our premises, we should instead place them in the conclusion, because it's the auxiliary hypotheses that actually impregnate our observations with the theory necessary to make them possible at all. To preserve the validity of the argument, then, we append the auxiliary hypotheses to 'E' as the antecedent of a material implication.

H ⊨ (A^1 & ... A^n) → E

In this case, a falsifying observation is characterised as the negation of a material implication. 'Not-E' alone is not something which can be observed, because an observation-report is a complex theoretical entity that incorporates the auxiliary hypotheses. The observation, for example, 'there is a cup of water here on the table', can be false in many different ways, but each way that it might be false changes the meaning of the observation in some way.

For example, suppose 'not-E' is true. This does not necessarily falsify 'H', because the argument remains valid if we assume that 'A1 & ... An' is false. This is another manifestation of the Duhem-Quine thesis. However, in this new formulation of the argument, assuming the auxiliary hypotheses are false is tantamount to claiming the observation itself is false, because it's the auxiliary hypotheses that are doing the theoretical-ladening--they are what make the observation possible in the first place.

So constructed, the target of a falsifying observation is no longer ambiguous. If the conclusion is false then 'H' must also be false. To evade falsification, one instead has to deny that the observation is true. This is, of course, a logically permissible move, but it isolates disagreement in the theoretical interpretation of an observation.

OPERA had a not-E result, in that the detection was slightly too soon (actually a loose wire delayed a timing signal).

That raised the possibility of not-H, but eventually not-A[1] was demonstrated. They did examine each A[i] and found one that was false; fixed it; and finished with E=true.

If I understand your conclusion, only after OPERA had satisfied themselves of each A[i] could they conclude not-H. In fact, that was the attitude of the cooler heads in that early discussion; in contrast to a too-quick "we've discovered faster-than-light neutrinos" view.

There were multiple interpretations of the evidence on the table. One interpretation was that a faster than light neutrino had been observed, and another was that an equipment malfunction had been observed. The immediate experience was of the same outputs on a computer screen, but depending on which assumptions you bring, you'll report a different observation.

There is little ambiguity about what those observations, if true, entail about different scientific theories. The question, rather, is which interpretation is correct, and how can they be independently tested. In this case, a simple check of the equipment revealed a loose wire that explained the anomalous measurement.

The point I'm trying to make here is just that the Duhem-Quine thesis is often expressed in a way as though observation were not theory-laden--as though an observation were possible without auxiliary hypotheses. This leads to a misleading way of framing the thesis and a mischaracterisation of the logic of falsifiability.

The point I'm trying to make here is just that the Duhem-Quine thesis is often expressed in a way as though observation were not theory-laden--as though an observation were possible without auxiliary hypotheses. This leads to a misleading way of framing the thesis and a mischaracterisation of the logic of falsifiability.

Sadly, your scheme does not rescue the logic of falsification. The reason is that it's not possible to enumerate all auxiliary assumptions and thereby elucidate the extent of the theory-ladenness of the observation as per your logical schema. Imagine a logician interrupting a physicist of the 19th Century who was explaining the laws of motion by saying "well that's all only true if you assume that time is independent of the motion of the observer". The physicist would have scoffed and protested that the logician was a ridiculous pedant whose head was stuck in philosophical dreamland. Such an auxiliary hypothesis was well beyond any imaginable consideration at the time. The list of apparently unquestionable assumptions behind each scientific observation made is endless. How about this one for example - a mysterious, previously unknown class of undetectable particles does not synchronously interfere with all known neutrino speed experiments causing misidentification of particles and speeds.

Having said that, falsification is still a very useful tool of the trade of science, and your formulation could also be useful as a guide to using the tool. A scientist may have a good "hunch" of what the most shaky auxiliary assumptions are and how to test each of them. If so, according to your formulation, an unexpected observation should give cause to test each of its auxiliary hypothetical antecedents before the scientist can be confident that the theoretical hypothesis is false.

Falsification as logic, in the strict mathematical sense however is doomed. Identifying science with logic or mathematics is the source of most of science's past philosophical trauma in my view.

(By the way I believe Quine's argument followed these lines as well. The auxiliary hypotheses of any observation must include the entirety of science.)

Falsification as logic, in the strict mathematical sense however is doomed. Identifying science with logic or mathematics is the source of most of science's past philosophical trauma in my view.

I agree with you. I don't believe that science can be reduced to logic or mathematics, but rather must involve extra-logical rules. Methodology, social institutions, and perhaps even ethics are an important part of the scientific enterprise and irreducible to pure logic. There is no effective method, in the logician's sense, for discovering scientific knowledge. However, there's still a logic to science, much as there is a logic to the game of chess, to borrow Popper's example.

My purpose with this post was to critique the Duhem-Quine thesis.

The Duhem-Quine thesis is that it's impossible to test a scientific hypothesis in isolation, because any empirical test requires implicit auxiliary hypotheses.

I believe this is mistaken. It's mistaken because any test statement, such as 'there is a faster than light neutrino', is theory-laden. Such an observation isn't possible except in the context of a complex web of auxiliary hypotheses, including many that we're scarcely aware of. However, the Duhem-Quine thesis, as ordinarily presented, divorces the auxiliary hypotheses from the observation.

When auxiliary hypotheses are given their rightful place as part of the observation, there is no logical ambiguity about falsification--if the falsifying observation is true, then the hypothesis must be false. For example, one can no longer accept the falsifying observation and protect the tested hypothesis by revising auxiliary hypotheses instead, because by revising the auxiliary hypotheses one also denies the observation is true.

Sadly, your scheme does not rescue the logic of falsification. The reason is that it's not possible to enumerate all auxiliary assumptions and thereby elucidate the extent of the theory-ladenness of the observation as per your logical schema.

Why would our ability to enumerate the auxiliary hypotheses have anything to do with the logic? I can't enumerate the set of natural numbers, but I can still reason about the set of natural numbers. In fact, I assume we're unaware of most of our auxiliary hypotheses, and we're infinitely ignorant of their class of logical consequences. Furthermore, whether or not we can quantify theory-ladenness, or whether that even matters, is quite irrelevant to my purpose. I might well have assumed, for argument's sake, that all observation is equally theory-laden.

Imagine a logician interrupting a physicist of the 19th Century who was explaining the laws of motion by saying "well that's all only true if you assume that time is independent of the motion of the observer". The physicist would have scoffed and protested that the logician was a ridiculous pedant whose head was stuck in philosophical dreamland.

Well, yes, but it doesn't really pertain to my argument.

Such an auxiliary hypothesis was well beyond any imaginable consideration at the time. The list of apparently unquestionable assumptions behind each scientific observation made is endless. How about this one for example - a mysterious, previously unknown class of undetectable particles does not synchronously interfere with all known neutrino speed experiments causing misidentification of particles and speeds.

Yes, I know. Ironically, what you're saying here was part of the auxiliary hypotheses of my argument, and they were assumptions that I was aware of. I'm struggling to figure out why you believe they constitute a criticism.

(By the way I believe Quine's argument followed these lines as well. The auxiliary hypotheses of any observation must include the entirety of science.)

Right, but usually the Duhem-Quine thesis is presented apart from Quine's holism, because a lot of people would accept the former but not the latter.

Why would our ability to enumerate the auxiliary hypotheses have anything to do with the logic? I can't enumerate the set of natural numbers, but I can still reason about the set of natural numbers.

Ok please define for me precisely what an auxiliary hypothesis is and construct a test for determining whether a given statement about the Universe is a member of the relevant class of auxiliary hypotheses. You can reason logically about the natural numbers because they are constructible axiomatically.

Furthermore, whether or not we can quantify theory-ladenness, or whether that even matters, is quite irrelevant to my purpose. I might well have assumed, for argument's sake, that all observation is equally theory-laden.

I understand that theory-ladenness of observation is the primary point of the argument. I concur with the spirit of the argument. I'm simply expressing caution of tying this to a strict "logic" as you appeared to do above. Perhaps your "logic" was only meant to be illustrative rather than strict. Since we are in agreement about the danger of conflating the illustrativeness of scientific argument with logical strictness, consider me the logical pedant here if you wish, reinforcing the importance of differentiating the two.

NB How I roll with discussion : I assume the other person is highly intelligent and once I am satisfied that the other person must therefore be able to see my point and I see theirs, I'd rather go and do some more reading than engage in unnecessary contest.

Popper stressed that all observation is theory-laden. He argued that even a simple statement like 'there is a cup of water here on the table' is theoretically-loaded. Things like tables, water, and cups are defined by their general behaviour; even the idea of something being here involves rather complex assumptions about space and time.

So, we can identify 'E' with 'there is a cup of water here on the table', and we can identify 'A1 & ... An ' with hypotheses about water, cups, tables, space, time, and so forth. All these auxiliary hypotheses are necessary to make the observation-report 'there is a cup of water here on the table' possible; they are what make this a statement about the world and not just a meaningless string of letters. The only catch is that the auxiliary hypotheses do not, themselves, entail this statement. For that, you need to add 'H' to the mix--the hypothesis being tested.

So what if 'there is a cup of water here on the table' were false? In that case, either 'H' is false or at least one of the auxiliary hypotheses is false. However, if we falsify one of the auxiliary hypotheses, such as our general expectations of how tables behave, then our interpretation of the evidence must change too, and we have a different observation than before.

Take the example of faster than light neutrinos. When the scientists read the numbers off the computer monitor, there were two competing observations. One was that a faster than light neutrino had been observed, and the other was that an equipment malfunction had been observed. They were different observations because they assumed different auxiliary hypothesis; it's the auxiliary hypotheses about the numbers on the screen that make the observation.

The observation of the faster than light neutrino unambiguously falsified particular scientific theories, while the observation of faulty equipment didn't falsify anything important. In this case, it was possible to test the interpretations themselves, and a loose wire was discovered that explained the anomalous results.

Thanks for your response. It seems I was confusing two similar, yet quite different observations.

On the one hand, we can have the observation that ~E (that the observation 'there is a cup of water here on the table' is false, say) and this can be false in many ways: if any of the auxiliary hypotheses is false or if H is false or any combination thereof (there are in general ∑(Choose(n+1,1) from 1 to n+1) ways in which this can happen).

On the other hand, we can have the observation that ~E be a falsifying observation. That is, the ~E is such that all the auxiliary hypotheses are true. Which leads us to conclude that H must be false. And there is only one way in which this can happen.

The DQ thesis is, as you state, that no hypothesis can be tested in isolation. Your proposal (for circumventing DQ? I'm not sure what your goal is here) at the end suggests that we "place [the auxiliary hypotheses] in the conclusion." If you do this, you are doing exactly what DQ says you must do from a methodological standpoint: reflect on the total outcome. As Quine likes to put it, when we conduct an experiment, we put our entire theoretical apparatus on the chopping block. But this is exactly what you would be doing by putting your hypotheses in the conclusion... So, what is your proposal for? Again, I don't think I get the point..

Also, I think there are two things to keep in mind about DQ and Popper's falsificiationism.

First, Popper often talks about "genuine" falsification. In one sense I'm sure that he wants to block cases of misleading "falsification," where the results of an experiment only appear to falsify a hypothesis, but they do not in fact do so (keep trivial reasons in mind here: things like errors in the experiment, contamination, etc.). But in another sense, he might technically be able to argue that "counterexamples" to his theory sponsored by DQ are in fact not genuine counterexamples because they are not genuine falsifiers. Perhaps a genuine falsifier has to be an outcome that indeed refutes (perhaps unknowingly) a hypothesis because all the auxiliary hypotheses are true (again, perhaps unknowingly). Of course this introduces an epistemic problem for Popper, in that we might never know if the negative outcome of our experiment was a genuine or misleading falsifier, but it at least saves face against the logical problem.

Second, I think there is a way of understanding falsifiability not as a robust logical requirement, but more like a practical and contextual feature. For example, one of the cases Popper loves to talk about is Eddington's experiment that tested relativity. Popper suggests (and he is right to suggest) that if that experiment had not gone as planned, it would have refuted (in a practical sense, perhaps not a logical sense) Einstein's theory. It's true that, logically, the theory is isolated by possible auxiliary mistakes, but for all practical purposes, a negative result would have been fatal.

Now, if this is what falsifiability requires, then the DQ thesis is largely irrelevant, and is not a serious threat to Popper's view.. but it would also be true that falsificationism cannot claim to have provided a "deductive" standard for science..